\[J_{\frac{3}{4}}\left(z\right)=-2^{-\frac{1}{4}}\pi^{-\frac{1}{2}}z^{-\frac{3}{%
4}}\left(W'\left(0,2z^{\frac{1}{2}}\right)-W'\left(0,-2z^{\frac{1}{2}}\right)%
\right),\]